The basic properties of positive integral exponents form the definitions for the use of rational numbers as exponents.

Question

Quizplus · Accepted Answer

The use of rational numbers as exponents follows from the basic properties of positive integral exponents. For example, if we know that a^m * a^n = a^(m+n) for positive integral exponents m and n, then we can extend this property to rational exponents by defining a^(p/q) * a^(r/s) = a^((ps+qr)/(qs)), where p, q, r, and s are positive integers. Similarly, we can define a^(p/q)^r/s = a^((pr)/(qs)), using the property that (a^m)^n = a^(mn) for positive integral exponents m and n.

The Basic Properties of Positive Integral Exponents Form the Definitions